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・ Diriangén FC
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・ Dirichlet (crater)
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・ Dirichlet beta function
・ Dirichlet boundary condition
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Dirichlet integral
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・ Dirichlet's principle
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・ Dirichlet's theorem
・ Dirichlet's theorem on arithmetic progressions
・ Dirichlet's unit theorem
・ Dirichlet-multinomial distribution


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Dirichlet integral : ウィキペディア英語版
Dirichlet integral

In mathematics, there are several integrals known as the ''Dirichlet integral'', after the German mathematician Peter Gustav Lejeune Dirichlet.
One of those is
: \int_0^\infty \frac\,d\omega = \frac
This integral is not absolutely convergent, and so the integral is ''not even defined'' in the sense of Lebesgue integration, but it ''is'' defined in the sense of the improper Riemann integral or the Henstock–Kurzweil integral.〔Robert G. Bartle, (Return to the Riemann Integral ), ''The American Mathematical Monthly'', vol. 103, 1996, pp. 625-632.〕 The value of the integral (in the Riemann or Henstock sense) can be derived in various ways. For example, the value can be determined from attempts to evaluate a double improper integral, or by using differentiation under the integral sign.
== Evaluation ==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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